Numerical Analysis (Available Titles CengageNOW) 8th Edition solutions

Numerical Analysis (Available Titles CengageNOW) 8
Use the Bisection method to find p3 for f (x) = x cos x on [0, 1].

Numerical Analysis (Available Titles CengageNOW) 8
Let f (x) = 3(x + 1)(x 1 2 )(x 1). Use the Bisection method on the following intervals to find p3. a. [2, 1.5] b. [1.25, 2.5]

Numerical Analysis (Available Titles CengageNOW) 8
Use the Bisection method to find solutions accurate to within 102 for x 3 7x 2 + 14x 6 = 0 on each interval. a. [0, 1] b. [1, 3.2] c. [3.2, 4]

Numerical Analysis (Available Titles CengageNOW) 8
Use the Bisection method to find solutions accurate to within 102 for x 4 2x 3 4x 2 + 4x + 4 = 0 on each interval. a. [2, 1] b. [0, 2] c. [2, 3] d. [1, 0]

Numerical Analysis (Available Titles CengageNOW) 8
Use the Bisection method to find solutions accurate to within 105 for the following problems. a. x 2x = 0 for 0 x 1 b. ex x 2 + 3x 2 = 0 for 0 x 1 c. 2x cos(2x) (x + 1)2 = 0 for 3 x 2 and 1 x 0 d. x cos x 2x 2 + 3x 1 = 0 for 0.2 x 0.3 and 1.2 x 1.3

Numerical Analysis (Available Titles CengageNOW) 8
Use the Bisection method to find solutions accurate to within 105 for the following problems. a. 3x ex = 0 for 1 x 2 b. x + 3 cos x ex = 0 for 0 x 1 c. x 2 4x + 4 ln x = 0 for 1 x 2 and 2 x 4 d. x + 1 2 sin x = 0 for 0 x 0.5 and 0.5 x 1

Numerical Analysis (Available Titles CengageNOW) 8
a. Sketch the graphs of y = x and y = 2 sin x. b. Use the Bisection method to find an approximation to within 105 to the first positive value of x with x = 2 sin x.

Numerical Analysis (Available Titles CengageNOW) 8
a. Sketch the graphs of y = x and y = tan x. b. Use the Bisection method to find an approximation to within 105 to the first positive value of x with x = tan x.

Numerical Analysis (Available Titles CengageNOW) 8
a. Sketch the graphs of y = ex 2 and y = cos(ex 2). b. Use the Bisection method to find an approximation to within 105 to a value in [0.5, 1.5] with ex 2 = cos(ex 2).

Numerical Analysis (Available Titles CengageNOW) 8
Let f (x) = (x +2)(x +1)2 x(x 1)3(x 2). To which zero of f does the Bisection method converge when applied on the following intervals? a. [1.5, 2.5] b. [0.5, 2.4] c. [0.5, 3] d. [3, 0.5]

Numerical Analysis (Available Titles CengageNOW) 8
Let f (x) = (x +2)(x +1)x(x 1)3(x 2). To which zero of f does the Bisection method converge when applied on the following intervals? a. [3, 2.5] b. [2.5, 3] c. [1.75, 1.5] d. [1.5, 1.75]

Numerical Analysis (Available Titles CengageNOW) 8
Find an approximation to 3 correct to within 104 using the Bisection Algorithm. [Hint: Consider f (x) = x 2 3.]

Numerical Analysis (Available Titles CengageNOW) 8
Find an approximation to 3 25 correct to within 104 using the Bisection Algorithm.

Numerical Analysis (Available Titles CengageNOW) 8
Use Theorem 2.1 to find a bound for the number of iterations needed to achieve an approximation with accuracy 103 to the solution of x 3+x4 = 0 lying in the interval [1, 4]. Find an approximation to the root with this degree of accuracy.

Numerical Analysis (Available Titles CengageNOW) 8
Use Theorem 2.1 to find a bound for the number of iterations needed to achieve an approximation with accuracy 104 to the solution of x 3x1 = 0 lying in the interval [1, 2]. Find an approximation to the root with this degree of accuracy.

Numerical Analysis (Available Titles CengageNOW) 8
Let f (x) = (x 1)10, p = 1, and pn = 1 + 1/n. Show that | f (pn )| < 103 whenever n > 1 but that |p pn | < 103 requires that n > 1000

Numerical Analysis (Available Titles CengageNOW) 8
Let {pn } be the sequence defined by pn = n k=1(1/k). Show that {pn } diverges even though limn(pn pn1) = 0.

Numerical Analysis (Available Titles CengageNOW) 8
The function defined by f (x) = sin x has zeros at every integer. Show that when 1 < a < 0 and 2 < b < 3, the Bisection method converges to a. 0, if a + b < 2 b. 2, if a + b > 2 c. 1, if a + b = 2

Numerical Analysis (Available Titles CengageNOW) 8
A trough of length L has a cross section in the shape of a semicircle with radius r (see the accompanying figure). When filled with water to within a distance h of the top, the volume V of water is V = L  0.5r 2 r 2 arcsinh r  h(r 2 h2 ) 1/2 . Suppose L = 10 ft, r = 1 ft, and V = 12.4 ft3. Find

Numerical Analysis (Available Titles CengageNOW) 8
A particle starts at rest on a smooth inclined plane whose angle is changing at a constant rate d dt = < 0. At the end of t seconds, the position of the object is given by x(t) u(t) x(t) = g 22 ewt ewt 2 sin t  . Suppose the particle has moved 1.7 ft in 1 s. Find, to within 105, the rate at w